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The Standard Model of particle physics is physics' best approximation to a complete theory of reality. It describes dozens of particles and the interactions between them, which fall into three categories; the strong nuclear force, the weak nuclear force, and electromagnetism. The particles fit into two classes: bosons or ferimons.
Fermions include the familiar proton and neutron (both of which are composed of quarks, neutrinos, and gluons), and the electron, which is fundamental.
Bosons mediate interactions between fermions.
The main difference between bosons and fermions is that bosons can share the same quantum state, whereas fermions cannot. The Standard Model is routinely used to predict the outcomes of interactions between particles to many significant figures of accuracy. It is not entirely complete, but is the best theory around since its inception between 1970 and 1973.
Fermions consist of 6 quark varieties and 6 lepton varieties. Nearly all matter we observe around us consists of 2 quark types, the "up" quark and the "down" quark, and 1 lepton variety, the electron. These three particles are sufficient to make up all the atoms in the Periodic Table, and the molecules they create when bonded to one another. The remaining 4 quarks and 5 leptons are more massive versions which otherwise behave the same as their less massive cousins. They can be created in high-energy physics experiments for split-second periods. Every lepton has a neutrino (energy-carrying particle of extremely low mass and high velocity) that corresponds to it. All of these particles also have antimatter versions, which behave in the same way, but annihilate upon contact with non-antimatter, converting the mass of both particles into pure energy.
Bosons come in 4 varieties, which mediate the three fundamental forces mentioned earlier. The most familiar boson is the photon, which mediates electromagnetism. This is responsible for all the phenomena surrounding electricity, magnetism, and light. Other bosons include the W and Z bosons, which mediate the weak nuclear force; and gluons, which mediate the strong nuclear force that binds quarks together into larger particles such as neutrons and protons. In this way The Standard Model explains or unites 3 of the 4 fundamental forces in nature; the outstanding force being gravity.
The Higgs boson is a boson whose existence is predicted by the Standard Model but has not yet been observed. It would be responsible for the mechanism by which all the particles acquire mass. Another hypothetical boson is the graviton, which would mediate gravitational interactions.
Gravity is not included in the Standard Model because we lack a theoretical description or experimental clues of the bosons which mediate gravitational interactions. However, modern string theory has introduced intriguing possibilities for further exploration into possible ways to expose the hypothetical graviton. If one day successful, it may turn out to replace The Standard Model by uniting all 4 fundamental forces, hence becoming the elusive "Theory of Everything."